论文标题
FLRW宇宙学的保形结构：旋转表示和SO（3,2）代数
Conformal structure of FLRW Cosmology: Spinorial representation and the so(3,2) algebra of observables
论文作者
论文摘要
最近显示，与一般相对论相连的无质量标量场的均质和各向同性宇宙学在适当时间的Mobius转换下表现出新的隐藏的保形不变性，此外还显示了时间逆转下的不变性。由此产生的Noether电荷形成了$ SL（2，\ Mathbb {r}）$ lie代数，该代数封装了几何学的整个运动学和动力学。这允许将FLRW宇宙学映射到保形力学上，并在$ \ text {cft} _1 $项中制定量子宇宙学。在这里，我们表明，这种保形结构嵌入了较大的$ $ so（3,2）$代数的观测值，它允许在整个重力和统一图片中呈现所有重力的所有狄拉克可观察物。这不仅允许人们量化系统及其整个观测值的代数为$ SO（3,2）$的单个不可约表示，但这也可以访问标量场操作员$ \ hat ϕ $为标量领域的非平凡潜力打开大门。因此，这种扩展的保形结构可能允许对通货膨胀宇宙学背景进行群体量化。
It was recently shown that the homogeneous and isotropic cosmology of a massless scalar field coupled to general relativity exhibits a new hidden conformal invariance under Mobius transformation of the proper time, additionally to the invariance under time-reparamterization. The resulting Noether charges form a $sl(2,\mathbb{R})$ Lie algebra, which encapsulates the whole kinematics and dynamics of the geometry. This allows to map FLRW cosmology onto conformal mechanics and formulate quantum cosmology in $\text{CFT}_1$ terms. Here, we show that this conformal structure is embedded in a larger $so(3,2)$ algebra of observables, which allows to present all the Dirac observables for the whole gravity plus matter sectors in a unified picture. Not only this allows one to quantize the system and its whole algebra of observables as a single irreducible representation of $so(3,2)$, but this also gives access to a scalar field operator $\hatϕ$ opening the door to the inclusion of non-trivial potentials for the scalar field. As such, this extended conformal structure might allow to perform a group quantization of inflationary cosmological backgrounds.
